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- Dmitry E Pelinovsky, Andrey A Sukhorukov, Yuri S Kivshar
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2004

We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear SchrÃ¶dinger equation with a sinusoidal potential, such as photonicâ€¦ (More)

Spectral stability analysis for solitary waves is developed in the context of the Hamiltonian system of coupled nonlinear SchrÃ¶dinger equations. The linear eigenvalue problem for a non-self-adjointâ€¦ (More)

- Yue Liu, Dmitry E Pelinovsky, Anton Sakovich
- SIAM J. Math. Analysis
- 2010

The Ostrovskyâ€“Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion. Sufficient conditions for the wave breaking in theâ€¦ (More)

Abstract Based on the recent work [4] for compact potentials, we develop the spectral theory for the one-dimensional discrete SchrÃ¶dinger operator HÏ† = (âˆ’âˆ† + V )Ï† = âˆ’(Ï†n+1 + Ï†nâˆ’1 âˆ’ 2Ï†n) + VnÏ†n. Weâ€¦ (More)

- Dmitry E Pelinovsky, Yury A. Stepanyants
- SIAM J. Numerical Analysis
- 2004

Abstract. We analyze a heuristic numerical method suggested by V.I. Petviashvili in 1976 for approximation of stationary solutions of nonlinear wave equations. The method is used to constructâ€¦ (More)

We give an overview of the basic physical concepts and analytical methods for investigating the symmetrybreaking instabilities of solitary waves. We discuss self-focusing of spatial optical solitonsâ€¦ (More)

Wave group dynamics is studied in the framework of the extended Korteweg-de Vries equation. The nonlinear Schrodinger equation is derived for weakly nonlinear wave packets, and the condition forâ€¦ (More)

Transmission of coherent light through photonic gratings with varying Kerr nonlinearity is modeled within a coupled-mode system derived from the Maxwell equations. The incident light waves areâ€¦ (More)

We reformulate the Grossâ€“Pitaevskii equation with an external parabolic potential as a discrete dynamical system, by using the basis of Hermite functions. We consider small amplitude stationaryâ€¦ (More)

The dynamics of a one-dimensional slowly modulated, nearly monochromatic localized wave train in deep water is described by a one-dimensional soliton solution of a twodimensional nonlinearâ€¦ (More)